Practice Questions on Engineering Mathematics

Q1.

 The function $ 2x^2-9x-2 $ has a minimum value in the interval [2,6]   at:

A.

$\dfrac{7}{4}  $.

B.

$\dfrac{9}{4}  $.

C.

$\dfrac{5}{4}  $.

D.

$\dfrac{3}{4}  $.

 View Ans

Q2.

The order of the differential equation,
\[\dfrac{d^3y}{dx^3}+\left(\dfrac{dy}{dx}\right)^3+x^2+y^4=0\]

A.

4

B.

3

C.

2

D.

1

 View Ans

Q3.

The value of line integral \(\int_{c}^{}(3x-y)ds\) and $C$ is the portion of the circle \(x^2+y^2=18\) traversed from (-3, 3) counterclockwise around to (3, 3) followed by the line segment from (3, 3) to (1, 2) is:

A.

\(54\sqrt{2}+\dfrac{11\sqrt{5}}{2}\)

B.

\(24\sqrt{3}+\dfrac{7\sqrt{5}}{2}\)

C.

\(23\sqrt{2}+\dfrac{9\sqrt{5}}{2}\)

D.

\(54\sqrt{2}+\dfrac{7\sqrt{5}}{2}\)

 View Ans

Q4.

Given the shape of helix defined by

\(x=2\cos t,\;y=t,\;z=2\sin t\)

where \(0\leq t\leq 6\pi\) and mass density \(\rho(x,y,z)=y\)

A.

\(24\pi^2 \sqrt{6}\)

B.

\(36\pi^2 \sqrt{6}\)

C.

\(24\pi^2 \sqrt{5}\)

D.

\(18\pi^2 \sqrt{5}\)

 View Ans

Q5.

If $ f(x)=|\cos x| $; then the Fourier series coefficient $ a_{0} $ and $ b_{0} $ is:

A.

$ 4/3\pi,\;0 $

B.

$ 4/\pi,\;0 $

C.

$ 1/3\pi,\;2/3\pi $

D.

$ 5/5\pi,\;4/3\pi $

 View Ans


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